Slide edges with absolute values
The quickest way would depend, not on whether the cylinder-object is aligned to the world axes, but on whether the cylinder's mesh is aligned to its own Object (Local) axes.

If the cylinder is aligned to its own axes:


For an absolute length, you can set its size in that dimension in the 'Dimensions' panel of the properties region of the 3D View, in Object Mode. Beware. This will scale the object's transform matrix. It's probably desirable to  CtrlA > Apply the scale, to bake it into the mesh.
To move one end by a numerically entered amount in Edit Mode, you can just set your Transform Orientation to 'Local' , and (supposing the cylinder was created with Z along its length) hit  GZZ [the number].


If the cylinder is not aligned to its own axes:


You can create a Custom Orientation from a longitudinal edge. Select the edge, and hit CtrlAltSpace.  (I usually check 'Use after Creation' and 'Overwrite Previous'.) Now any translation or scale you make with GYY or SYY will be in that edge's direction, and will accept numerical entries.


For absolute transforms, you can always create a jig. Just duplicate, for example,  a single vertex at a known zero point, then transform it to the full extent numerically in the desired Transform Orientation, and use it as a snap target for translation, scale, or rotation, before deleting it.